Paul suffered the injury when he crashed to the floor after being fouled by Dallas guard Monta Ellis with 6:43 remaining in the third quarter. The Clippers announced Paul was out for the game minutes later.
Clippers coach Doc Rivers later clarified the injury to the star's right, shooting arm was a separated shoulder after the team had announced it was a sprain.
Different from a dislocated shoulder, a separated shoulder is a tear to one of the connecting ligaments between the collarbone and shoulder blade.
Paul left the American Airlines Center with his right arm in a sling and did not speak to the media.
"He's down," Rivers said. "He's out at least three to five weeks and maybe more. We don't know that [yet]. We know it's a separated shoulder. We don't know what grade it is, yet. We'll probably send him home, and he'll get evaluated in L.A., and just hope that he's going to be OK."
The Clippers later said Paul would be with the team in San Antonio on Saturday and would be examined in L.A. on Sunday. He is scheduled to visit a specialist Monday. After that, the team will provide an update on the injury and a recovery schedule.
Paul, an All-Star the past six seasons, is averaging 19.6 points and a league-high 11.2 assists per game. Darren Collison, who signed a two-year, $3.9 million deal this summer to back up Paul after spending last season in Dallas, had 20 points and four assists while playing 35 minutes in the win against the Mavs.
Collison is averaging 8.5 points and 2.1 assists in 18.9 minutes per game this season.
"It's going to be tough because he's our engine," Collison said. "He's our leader. He does a lot for us. But at the same time, this team is very talented. We have the depth to overcome this. We're only hoping that CP comes back as soon as possible."